On the choice of the time step and the probability of collision in numerical statistical modeling of particle transfer with an acceleration by an external force field (Q2254129)

The authors solve the problem of chosing the time step \(\Delta t\) in an algorithm for numerical statistical modeling of the transfer of charged particles under the influence of the interaction with particles of the medium and an external force field. The choice criterion is an appropriate deterministic error of statistical estimates of the integral characteristics under examination. As application, the evolution of electron avalanches in gases in an external electric field is considered. The mean number \(n\) of particles at a moment of time \(t\) for one initial particle, the mean kinetic energy \(T\), and the mean position of the center of mass \(z\) are calculated using different time steps \(\Delta t\). The results show that an assumed exponential interaction probability, underestimating the interaction, leads to an increase in \(n\) and \(T\). Replacing the probability by a step-like function containing a second-order term with respect to the interaction cross-section (Taylor series of second order) helps to essentially decrease the computational time. The selection of an appropriate coefficient of the square of the cross-section may decrease the relative deterministic error of the results.